Interference alignment for partially connected cellular networks

ABSTRACT

Interference alignment for a multiple-input multiple-output communications network with partial connectivity is provided. A method is provided that includes determining assignments for data streams transmitted in the multiple-input multiple-output communications network. The method also includes suppressing inter-cell interference and suppressing intra-cell interference. Also provided is inter-cell/intra-cell decomposition and exploitation of partial connectivity in a multiple-input multiple-output communications network. The multiple-input multiple-output communications network can comprise three or more cells.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a United States National Phase Application of, andclaims priority to each of, PCT Application Number PCT/CN2013/000165,filed on Feb. 21, 2013, and entitled “INTERFERENCE ALIGNMENT FORPARTIALLY CONNECTED CELLULAR NETWORKS”, which claims priority to U.S.Provisional Application No. 61/634,264, filed Feb. 27, 2012, andentitled “INTERFERENCE ALIGNMENT OF PARTIALLY CONNECTED MIMO CELLULARNETWORKS”, the entireties of which applications are hereby expresslyincorporated herein by reference.

TECHNICAL FIELD

This disclosure generally relates to wireless communications and, alsogenerally, to interference alignment for partially connected cellularnetworks.

BACKGROUND

The wide adoption of mobile devices along with ubiquitous cellular datacoverage has resulted in an explosive growth of mobile applications thatexpect always-accessible wireless networking. This explosion has placeddemands on network performance including demands for fast and reliablecommunication paths and for reduction of interference in the network. Onthe user side, instances of slow communication links and/orcommunication failures have been blamed for user dissatisfaction. On thenetwork side, the slow communication links and communication failurescan develop due to interference that has not been adequately mitigatedin the communications network.

The above-described background is merely intended to provide an overviewof information regarding the effects of interference within a wirelesscommunications network, and is not intended to be exhaustive. Additionalcontext may become apparent upon review of one or more of the variousnon-limiting embodiments of the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

Various non-limiting embodiments are further described with reference tothe accompanying drawings in which:

FIG. 1 are example, non-limiting cellular topologies that illustrateoverlapping and partial connectivity in cellular networks;

FIG. 2 are example, non-limiting cellular topologies that illustratedecomposition of inter-cell and intra-cell interference alignment inmultiple-input multiple-output cellular networks according to variousembodiments;

FIG. 3 illustrates an example, non-limiting embodiment of a wirelessnetwork that depicts subspace constraints exploiting partialconnectivity;

FIG. 4 is an example, non-limiting block diagram of a system configuredto reduce interference within a communications network in accordancewith an aspect;

FIG. 5 is an example, non-limiting block diagram of a system forinterference alignment, according to an aspect;

FIG. 6 is an example, non-limiting method for interference alignment ofpartially connected multiple-input multiple-output cellular networks,according to an aspect;

FIG. 7 illustrates an example, non-limiting embodiment of a method formitigation of interference in a communications network;

FIG. 8 is a schematic example communications environment that canoperate in accordance with aspects described herein;

FIG. 9 illustrates a block diagram of access equipment and/or softwarerelated to access of a communications network, in accordance with anembodiment; and

FIG. 10 illustrates a block diagram of a computing system, in accordancewith an embodiment.

DETAILED DESCRIPTION

Aspects of the subject disclosure will now be described more fullyhereinafter with reference to the accompanying drawings in which exampleembodiments are shown. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea thorough understanding of the various embodiments. However, thesubject disclosure may be embodied in many different forms and shouldnot be construed as limited to the example embodiments set forth herein.

Various aspects disclosed herein relate to interference alignment (IA)for cellular networks. In an aspect, the cellular network can be amultiple-input multiple-output (MIMO) cellular network that comprisespartial connectivity. Partial connectivity refers to the scenario inwhich channel matrices between base stations and mobile devices in thenetwork are not full rank. The term “rank” refers to a measure of thecapacity of a channel. MIMO cellular networks can introduce severaltechnical challenges as it relates to IA. For example, overlapping thatoccurs between direct links and interfering links due to the MIMOcellular topology can negatively affect IA. Further, the partialconnectivity that occurs within the network and how to deal with thepartial connectivity can negatively affect IA.

The disclosed aspects address the above, as well as other issuesassociated with IA in cellular networks, through an IA process. In animplementation, the IA process can be a three-stage IA process. Alsoprovided herein is an analysis of the achievable degree of freedom (DoF)of the disclosed aspects for a symmetric partially connected MIMOcellular network. As will be discussed herein, the disclosed aspects canprovide a DoF gain as compared with other IA processes. The DoF gain(which can be a significant gain according to some aspects) can beattributable, at least in part, to using partial connectivity as anadvantage with the disclosed IA processes. According to some aspects,the derived DoF bound provided herein can be backward compatible with aDoF bound achieved on fully connected K-pair MIMO interference channels.

As previously mentioned, the wide adoption of mobile devices hasincreased the demand for always-accessible wireless networking. Thisdemand has brought about a corresponding interest in the area ofinterference channels and associated interference mitigation techniques.For example, IA approaches can be utilized to mitigate interference inK-pair interference channels. For example, when there are multiple nodessimultaneously transmitting, IA processing can align the interferencefrom different transmitters into a lower dimension subspace, which canprovide the receivers with one or more “clean” dimensions to decode thedesired signals. This in turn can improve system performance.

In one or more disclosed aspects, an IA approach can achieve an optimal,or near optimal, DoF in K-pair interference channels, as well as 2-pairMIMO-X channels. In an example, an IA approach can be extended tocellular OFDMA systems by exploiting a problem-specific structure, suchas the channel states being full-rank diagonal matrices. In anotherexample, the IA approach can be extended to MIMO cellular networks. Theextension of IA to MIMO networks have focused on two-cell configurationswith one data stream for each mobile station (MS), also referred toherein as mobile device or the like, or to a configuration with no morethan two mobile devices in each cell. The extension of IA to generalMIMO cellular networks (with an arbitrarily number of cells, mobiledevices, and data streams) has not previously been achievable.

Furthermore, some IA techniques assume a fully connected interferencetopology. In practice, however, there might be heterogeneous path lossesbetween base stations (BSs) and MSs as well as spatial correlation inthe MIMO channels. These physical effects induce a partially connectedinterference topology. Partial connectivity in interference topology maycontribute to limiting the aggregate interference and this may translateinto throughput gains in interference-limited systems. In order toexploit the partial connectivity in the channel as an advantage, thevarious aspects disclosed herein incorporate the partial connectivitytopology in an IA process. Therefore, the disclosed aspects overcomevarious features inherent to MIMO cellular networks, such as partialconnectivity and quasi-static fading, for example.

In an example, an IA process can be applied where interference channelscan take advantage of the statistical independency of the direct links(e.g., the links from the transmitter to an intended receiver) and thecross-links (e.g., the links from the transmitter to unintendedreceivers), which allows for such links to be distinguished from eachother. As a result, the IA process can achieve a defined (e.g., atarget) number of data streams per each direct link with probability one(1), provided the interference channel is IA feasible. However, for MIMOcellular networks, there is overlapping between the direct links and thecross-links. Due to the overlapping nature of the direct link and thecross-links, brute force application of some interference alignmentschemes in MIMO cellular systems may not result in the desiredperformance.

In another example, MIMO cellular systems can be partially connected dueto path losses and spatial correlation. While path losses and spatialcorrelation effects are undesirable for the direct links, they may alsocontribute to limiting the strength and the dimension of the aggregateinterference on the cross-links. In practice, however, many parametersare used to quantify path losses and spatial correlation. Theseparameters can vary (at time dramatically) according to differentphysical scenarios. Therefore, an IA process, which can exploit thebenefit of partial connectivity, is disclosed herein.

In a further example, some interference algorithms use infinitedimensions of signal space obtained through time-domain symbolextension, which is difficult to realize in practice. In one example, aninterference alignment feasibility-checking algorithm involves a hugecomplexity of O(2^(N) ² ), where N is the total number of nodes (e.g.,devices) in the network. This complexity is not tolerable in a practicalapplication. Therefore, provided herein is an IA algorithm that does notexploit symbol extension.

Disclosed herein is an IA approach that exploits the partialconnectivity topology in MIMO cellular networks. An optimization-basedapproach is used to decompose the IA process into three sub-processes,which overcomes the above noted issues and hence accommodates the MIMOcellular topology and the partial connectivity. Moreover, a lowcomplexity IA feasibility determination (e.g., checking algorithm) isprovided. For example, in an implementation, an algorithm that has aworst-case complexity of O(N³) only is provided. In view of thedisclosed aspects, an achievable bound on the DoF in a symmetricpartially connected MIMO cellular network is derived. Further, it isdemonstrated herein that by using the disclosed aspects, the partialconnectivity can be exploited to increase the total DoF in the MIMOcellular networks.

Referring initially to FIG. 1, example, non-limiting cellular topologiesare depicted that illustrate overlapping and partial connectivity incellular networks. As illustrated, a first topology 100 can include afirst base station 102 and a second base station 104. Also included canbe a first mobile device 106 and a second mobile device 108. The basestations and mobile devices in this example have two antennas each. Adirect link 110, between the first base station 102 and the first mobiledevice 106, carries a desired signal (e.g., the signal intended for thefirst base station 102 and the first mobile device 106). In a similarmanner, a direct link 112, between the second base station 104 and thesecond mobile device 108, carries a desired signal for the second basestation 104 and the second mobile device 108. Between the first basestation 102 and the second mobile device 108 is a cross-link 114, whichcarries an undesired signal. Further, between the second base station104 and the first mobile device 106 is a cross-link 116, which carriesan undesired signal.

The second topology 118 is illustrated as including a first base station120 and a second base station 122, having two antennas each. Further,the second topology 118 is illustrated as including a first mobiledevice 124, a second mobile device 126, a third mobile device 128, and afourth mobile device 130, having two antennas each.

Between the first base station 120 and the first mobile device 124 is afirst set of links 132, which carry two signals, which include thedesired signal (e.g., the symbols for the first mobile device 124) andan undesired signal (e.g., the symbols for the second mobile device126). Further, a second set of links 134, between the first base station120 and the second mobile device 126, carry two signals, which include adesired signal (e.g., symbols for the second mobile device 126) and anundesired signal (e.g., symbols for the first mobile device 124).

In a similar manner, a third set of links 136 between the second basestation 122 and the third mobile device 128 carry both a desired signal(e.g., symbols for the third mobile device 128) and an undesired signal(e.g., symbols for the fourth mobile device 130). In addition, a fourthset of links 138 between the second base station 122 and the fourthmobile device 130 carry both a desired signal (e.g., symbols for thefourth mobile device 130) and an undesired signal (e.g., symbols for thethird mobile device 128).

Further, due to the broadcast nature of the transmissions, the firstbase station 120 sends a first undesired link 140 to the third mobiledevice 128 and a second undesired link 142 to the fourth mobile device130. In a similar manner, the second base station 122 sends a thirdundesired link 144 to the first mobile device 124 and a fourth undesiredlink 146 to the second mobile device 126.

As discussed with reference to FIG. 1, in point-to-point networks, alink carries either a desired signal or an undesired signal. However, incellular networks, intra-cell links carry both desired signals andundesired signals. Since the two types of links (e.g., the link carryingthe desired signal and the link carrying the undesired signal) areoverlapped, when minimizing the interference leakage according to thechannel state information of cross-links, at least a portion of thedesired signals on the direct links might be unintentionally cancelled.

FIG. 2 depicts example, non-limiting cellular topologies that illustratedecomposition of inter-cell and intra-cell IA in MIMO cellular networksaccording to various embodiments. FIG. 2 is similar to the secondtopology 118 of FIG. 1 and, therefore, for purposes of simplicity, thesame element numbers will be utilized. The left side of FIG. 2illustrates an inter-cell IA topology 202 and the right side of FIG. 2illustrates an intra-cell IA topology 204 for the first base station 120and an intra-cell IA topology 206 for the second base station 122.

As illustrated by the inter-cell IA topology 202, by decomposing theinter-cell interference alignment, there is no overlap with the directlinks. Therefore, the inter-cell interface alignment can be handled witha basic iterative interference alignment process.

Further, the intra-cell interference alignment for each of the basestations is decoupled to a per-cell basis, illustrated by intra-cell IAtopology 204 and intra-cell IA topology 206. This decoupling to aper-cell basis can make the IA simpler to implement, according to anaspect.

According to one or more implementations, decomposition of theinter-cell and intra-cell IAs can be implemented through a structure ina precoder design. Further, partial connectivity can offer an additionalopportunity to cancel interference. Various implementations discussedherein exploit this opportunity under the IA framework by introducingsubspace constraints in a transceiver design. For example, FIG. 3illustrates an example, non-limiting embodiment of a wireless network300 that depicts subspace constraints exploiting partial connectivity.Illustrated are a first base station 302 and five mobile stations (MSs)labeled as first MS 304, second MS 306, third MS 308, fourth MS 310, andfifth MS 312. The arrows 314 and 316 depict the subspace constraintrestricted in the transmission direction. As discussed herein, theseconstraints can be designed such that a large fraction of interferenceis cancelled at a cost of slightly reducing the policy space oftransceiver design.

According to an implementation, FIG. 4 is an example, non-limiting blockdiagram of a system 400 configured to reduce interference within acommunications network. Interference not only limits the amount ofbandwidth available to each device, but it can also limit theperformance of each device. To reduce the amount of interference in thenetwork, the system 400 is configured to exploit partial connectivity ofthe network.

Included in system 400 is a network device 402, which can be any one ofa number of communication devices including, but not limited to, a basestation, a network node, a mobile device, and so forth. Thecommunications network can be a MIMO network, according to an aspect.Further, the communications network can comprise an arbitrary number ofcells, users, antennas, or combinations thereof. For example, thedisclosed aspects can be applied to a network, regardless of the numberof cells, users, and/or antennas. According to an implementation, thecommunications network comprises three or more cells (e.g., basestations), wherein the network device 402 communicates with each of thethree or more base stations.

The network device 402 can comprise at least one memory 404 that canstore computer executable components and instructions. The networkdevice 402 can also include at least one processor 406, communicativelycoupled to the at least one memory 404. Coupling can include variouscommunications including, but not limited to, direct communications,indirect communications, wired communications, and/or wirelesscommunications. The processor 406 can facilitate execution of thecomputer executable components stored in the memory 404. The processor406 can be directly involved in the execution of the computer executablecomponent(s), according to an aspect. Additionally or alternatively, theprocessor 406 can be indirectly involved in the execution of thecomputer executable component(s). For example, the processor 406 candirect one or more components to perform the operations.

It is noted that although one or more computer executable components maybe described herein and illustrated as components separate from thememory 404 (e.g., operatively connected to memory), in accordance withvarious embodiments, the one or more computer executable componentscould be stored in the memory 404. Further, while various componentshave been illustrated as separate components, it will be appreciatedthat multiple components can be implemented as a single component, or asingle component can be implemented as multiple components, withoutdeparting from example embodiments.

The network device 402 can be configured to receive, either directly orindirectly (e.g., through another component, through another device, andso forth) data streams 408 transmitted within the communicationsnetwork. The data streams 408 can include various types of communicationincluding voice, video, data, and so on. Although only a single datastream is illustrated, it is noted that any number of intra-cell datastreams can be received and processed by the network device 402according to various implementations. In an example, BSs only transmitdata to MSs that are associated with the BSs. Thus, the data streams areintra-cell data streams. However, these streams create both inter- andintra-cell interference.

A data stream manager 410 can be configured to evaluate the data streams408 and determine the feasibility of interference alignment (IA) withinthe communications network. In implementation, data stream manager 410can be configured to determine assignments for the data streams 408transmitted in the communications network. For example, an assignment(or stream assignment {d_(nj)}) can be utilized to maximize a sum of thedata stream numbers (e.g., degree of freedom (DoF)) of thecommunications network. According to an implementation, the data streammanager 410 can utilize a greedy stream assignment to assign the datastreams 408. Based in part on the assignments, the data stream manager410 can determine if it would be beneficial to apply IA in thecommunications network.

According to some implementations, the data stream manager 410 can beconfigured to initialize a stream assignment policy and determinewhether interference alignment can be applied to the data streams 408 inthe communications network. For example, initializing the streamassignment policy can include setting the stream assignment policy to bethe number of streams requested by each mobile device within thecommunications network.

An interference manager 412 can be configured to suppress inter-cellinterference 414 and intra-cell interference 416 caused by the datastream 408. The suppression of the inter-cell interference 414 and theintra-cell interference 416 can be performed independently, orconcurrently. According to an implementation, suppressing the inter-cellinterference 414 can comprise updating intermediate precoders anddecorrelators. In an example, precoders are used to exploit transmitdiversity by weighting each of the information streams. For example, atransmitter 418 can send the coded information to a receiver (e.g., basestation, mobile device, a network entity, and so forth), wherein theweighting can be utilized to mitigate interference. In another example,the decorrelators can be updated in order to reduce autocorrelation in asignal (or to reduce cross-correlation within a set of signals), whereinother aspects of the signal are not updated (e.g., are preserved). Theupdated decorrelators can also be communicated to one or more otherdevices by the transmitter 418.

Further to this implementation, after the intermediate precoders anddecorrelators are updated, the precoders can be adjusted (e.g., by theinterference manager 412) a second time to suppress the intra-cellinterference 416. The second adjustment to the precoders can be sent bythe transmitter 418 to one or more other devices. According to anotherimplementation, the inter-cell interference 414 and the intra-cellinterference 416 can be zero forced in order to cancel interference andfacilitate interference alignment.

For the following discussion, the notation a represents scalar, thenotation a represents vector, the notation A represents matrix, and thenotation A represents set/space. Further, the operator (⋅)^(T) denotestranspose, the operator (⋅)^(H) denotes hermitian, the operator rank (⋅)denotes rank, the operator trace (⋅) denotes trace, and the operator|(⋅)| denotes dimension (of a space). Further span ({a}) denotes thelinear space spanned by the vectors in {a}. In addition, span_(c) ({A})and span_(r)({A}) represent the space spanned by the column vectors andthe row vectors of A, respectively. Further, G(S,N) denotes theGrassmannian, which represents the space of all the S dimensionalsubspaces of the N dimensional space. It is also noted that R representsthe set of real numbers and C represents the set of complex numbers.

In an example, a MIMO system with G base stations (BSs), each of whichserves K mobile stations (MSs) is provided (as depicted by the secondtopology 118 of FIG. 1). It is noted that G and K are integers greaterthan or equal to one, and can be the same or different integers. Thenumber of antennas at BS-g is denoted by N_(g) ^(t) and the k-th MS ofBS-g is denoted by N_(gk) ^(r). Further, the number of data streamstransmitted to the k-th MS from BS-g is denoted by d_(gk). The receivedsignal at the k-th MS of BS-g can be given by:

$\begin{matrix}{{y_{gk} = {U_{gk}\left( {{\sum\limits_{n = 1}^{G}{H_{{gk},n}{\sum\limits_{i = 1}^{K}{V_{ni}x_{ni}}}}} + z} \right)}},{\forall{k \in {\left\{ {1,\ldots\mspace{14mu},K} \right\}.}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where H_(gk,n)∈C^(N) ^(gk) ^(r) ^(×N) ^(n) ^(t) is the channel stateinformation (CSI) from BS-n to the k-th MS from BS-g. Also, x_(ni)∈C^(d)^(ni) ^(×1), V_(ni)∈C^(N) ^(n) ^(t) ^(×d) ^(ni) , and U_(ni)∈C^(d) ^(ni)^(×N) ^(ni) ^(r) are the information symbols, the precoding matrix, andthe decorrelation matrix, respectively, for the i-th MS of the BS-g.Further, z∈C^(N) ^(gk) ^(r) ^(×1) is the zero mean white Gaussian noisewith unity variance. The CSI matrices {H_(gk,n)} are assumed to bequasi-static and mutually independent random matrices. Further, theprecoding matrix and the transmit symbols are normalized as trace(V_(ni)^(H)V_(ni))=d_(ni) and E[Σ_(i=1) ^(K)trace(x_(ni) ^(H)x_(ni))]=P_(n)such that the total transmit power from BS-n is P_(n).

As used herein, partial connectivity can be defined between BS-n and thek-th MS from BS-g as the null space and the “transposed” null space ofthe CSI H_(gk,n). The null space is given by N′(H_(gk,n)) @{u∈^(N) ^(n)^(t) :H_(gk,n)v=0}. The transposed null space is given by: N′(H_(gk,n))@{u∈^(N) ^(gk) ^(r) :u^(H)H_(gk,n)=0}.

Partial connectivity is utilized herein to describe (e.g., in thephysical sense) the effective subspaces of the channel matrices betweenBSs and MSs in the network. For example, the null spaces and thetransposed null spaces, {N(H_(gk,n)), N′(H_(gk,n))}, represent thesubspaces that cannot be perceived by the BSs and the MSs, respectively.Thus, the partial connectivity topology of the MIMO network isparameterized by the null spaces {N(H_(gk,n)), N′(H_(gk,n))}. Further,both the inter-cell inks (e.g., g≠n) and the intra-cell links (e.g.,g=n) may be partially connected.

A few examples, with reference to the second topology 118 of FIG. 1 areprovided to illustrate how the partial connectivity model, as describedabove, corresponds to various physical situations. For purposes of theseexamples, the third mobile device 128 is denoted as MS-21, the fourthmobile device 130 is denoted as MS-22, and the second base station 122is denoted as BS2. In these examples, the following is denoted:

$H_{{gk},n} = {\begin{bmatrix}{h_{{gk},n}(1)} & {h_{{gk},n}(2)} \\{h_{{gk},n}(3)} & {h_{{gk},n}(4)}\end{bmatrix}.}$

For a fully connected network (e.g., fully connected MIMO cellularnetwork), if h_(gk,n)(i),g∈1,2,k∈1,2,i∈{1,3,4} are independent randomvariables. This results in N(H_(gk,n))=N′(H_(gk,n))={0} and ∀g,k, whichcorresponds to a fully connected network.

As an example related to a MIMO cellular network with spatialcorrelation, the elements of H_(21,1) are correlated ash_(21,1)(1)=h_(21,1)(2), h_(21,1)(3)=h_(21,1)(4). This results inN(H_(21,1))=span_(c)([1,1]^(t)),

${N^{\prime}\left( H_{21,1} \right)} = {{{span}_{c}\left( \left\lbrack {1,{- \frac{h_{21,1}(1)}{h_{21,1}(3)}}} \right\rbrack^{t} \right)}.}$

For a MIMO cellular network with heterogeneous path losses, in anexample, the path loss from the first base station (BS-1) to the secondMS of the second base station (BS-2) is 60 dB and the transmit signal tonoise ratio (SNR) of BS-1 is 40 dB. The interference power from BS-1 canbe negligible as compared with the Gaussian noise, therefore, it can begiven that H_(21,1)=0, which results in N(H_(22,1))=N′(H_(22,1))=C², asillustrated in the second topology 118 of FIG. 1.

Stream assignment and transceiver design under IA constraints will nowbe described. It can be assumed that the BSs in the MIMO cellularnetwork share global channel state information (CSI) {H_(gk,n)}. Itshould be noted that global CSI can be fairly easy to obtain when thenetwork size is small. However, when the network size is large, thepartial connectivity can be exploited to achieve scalable CSI feedbackschemes, such as by utilizing a heterogeneous path loss, for example.

According to an implementation, an IA approach is used in order tomaximize the network total DoF, which can be defined by

${D = {\lim_{P->\infty}\frac{C}{\log(P)}}},$where C is the network sum throughput and P is the total transmit power.It is noted that, C=D log(P)+O(log(P)), DoF provides a first orderestimation on network throughput. Further, it can offer, at least somefirst order simplification to the complex throughput optimization on aMIMO interference network.

In accordance with an aspect, the data stream assignment {d_(nj)},precoders {V_(nj)}, and decorrelators {U_(nj)}, n∈{1, . . . , G}, . . ., j∈{1, . . . , K} policies are jointly optimized in order to maximizethe total number of data streams Σ_(n=1) ^(G)Σ_(k=1) ^(K)d_(nj) underthe IA constraints. For example, according to an implementation, theconstraints can be that the number of data streams is equal, or nearlyequal, to the DoF of the network.

A challenge associated with IA for MIMO cellular networks, therefore,can be expressed as:

$\begin{matrix}{\max\limits_{{\{ d_{nj}\}},{\{ V_{nj}\}},{\{ U_{gk}\}}}{\sum\limits_{n = 1}^{G}{\sum\limits_{j = 1}^{K}{d_{nj}.}}}} & {{Equation}\mspace{14mu} 2} \\{{{{s.t.\text{:}}\mspace{14mu}{{rank}\left( {U_{gk}H_{{gk},g}V_{gk}} \right)}} = d_{gk}},.} & {{Equation}\mspace{14mu} 3} \\{{{U_{gk}H_{{gk},n}V_{nj}} = 0},.} & {{Equation}\mspace{14mu} 4} \\{{{{trace}\left( {V_{nj}^{H}V_{nj}} \right)} = d_{nj}},{{.d_{nj}} \in \left\{ {0,1,\ldots\mspace{14mu},d_{nj}^{m\;{ax}}} \right\}},{\forall g},{n \in \left\{ {1,\ldots\mspace{14mu},G} \right\}},k,{j \in \left\{ {1,\ldots\mspace{14mu},K} \right\}},{\left( {n,j} \right) \neq {\left( {g,k} \right).}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$where d_(nj) ^(max) is the maximum number of data streams for theconcerned MS. Equation 3 helps to ensure that all the direct links havesufficient rank to receive the desired signals. Further, Equation 4helps to ensure that all the undesired signals are aligned and do notinterfere with the desired signals.

The following will solve the IA issue discussed above for fullyconnected MIMO cellular networks. Specifically, in a fully connectedMIMO cellular network, it can be assumed dim (N(H_(gk,n)))=(N_(n)^(t)−N_(gk) ^(r))+, and dim(N′(H_(gk,n)))=(N_(gk) ^(r)−N_(n) ^(t))+,where dim(X) denotes the dimension of subspace X, (a)⁺=max(α,0).

In MIMO cellular networks, an approach for IA for interference channelcan be based on the interference leakage minimization iteration, forexample. Although this approach might be designed for standardinterference channels, according to an aspect, the framework can beextended to a MIMO cellular network, as described below.

According to an example, to extend an iterative IA algorithm to MIMOcellular networks, precoders V_(nj) and decorrelators U_(gk) can bealternatively updated by minimizing total interference leakageexpressions (Equations 6 and 7 below) until the algorithm converges.

$\begin{matrix}{\min\limits_{\underset{{V_{nj}^{H}V_{nj}^{H}} = I}{V_{nj} \in C^{N_{n}^{t} \times d_{nj}}}}{\sum\limits_{g = 1}^{G}{\sum\limits_{\underset{{({g,k})} \neq {({n,j})}}{k = 1}}^{K}{{{trace}\left( {\left( {U_{gk}H_{{gk},n}V_{nj}} \right)^{H}\left( {U_{gk}H_{{gk},n}V_{nj}} \right)} \right)}.}}}} & {{Equation}\mspace{14mu} 6} \\{{\min\limits_{\underset{{U_{gk}U_{gk}^{H}} = I}{U_{gk} \in C^{d_{gk}N_{gk}^{r}}}}{\overset{G}{\sum\limits_{n = 1}}{\overset{K}{\sum\limits_{\underset{{({n,j})} \neq {({g,k})}}{j = 1}}}{{{trace}\left( {\left( {U_{gk}H_{{gk},n}V_{nj}} \right)^{H}\left( {U_{gk}H_{{gk},n}V_{nj}} \right)} \right)}.\mspace{20mu}{\forall n}}}}},{g \in \left\lbrack {1,\ldots\mspace{14mu},G} \right\}},j,{k \in {\left\{ {1,\ldots\mspace{20mu},K} \right\}.}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

The performance of the naive algorithm has been tested in a three-BSfully connected MIMO cellular network with K=2, N_(g) ^(t)=5, N_(gk)^(r)=2, d_(gk)=1, ∀g∈{1,3}, k∈{1,2}. It was shown that the naivealgorithm could achieve a total DoF of three (3), which is only half ofthe achievable DoF lower bound and demonstrates that naive extension ofan iterative IA algorithm might perform poorly in MIMO cellularnetworks. This poor performance can be attributable to the directlink/cross-link overlapping, as discussed above with reference to FIG.2, and which will be further defined below.

In an interference network, the set of channels that carry the desiredsignals can be denoted as H^(D) and the set of channels that carry theundesired signals can be denoted as H^(C). If H^(D)∩H^(C)≠Ø, then thenetwork has a direct link/cross-link overlap.

As illustrated in the first topology 100 of FIG. 1, in some MIMOinterference networks H^(D)={H_(mm)} and H^(C)={H_(mn):m≠n}, where m isthe index for the transmitters and n is the index for the receivers. Inthe illustrated example, H^(D)∩H^(C)=Ø and there are no overlappingissues. However, as illustrated in the second topology 118 of FIG. 1, ina MIMO cellular network, when the number of MSs per cell is more thanone (K>1), the intra-cell links also carry over undesired signals and,therefore, H^(D)={H_(gk,g)} and H^(C)={H_(gk,n)}. In this scenario,H^(D)∩H^(C)=H^(D)=Ø and the overlapping issue arises. In an example, asthe channel states in H^(D) appear (in Equations 6 and 7), the precodersand decorrelators can be updated (e.g., according to Equations 6 and 7).Further, the dimension of the signal space for the desired signals canalso be reduced.

According to an implementation, instead of a naive extension of aniterative IA algorithm, one or more of the disclosed aspects decomposethe issues associated with IA for MIMO cellular networks (e.g., withreference to Equations 2 through 5) into three sub-issues. For example,as illustrated by the example, non-limiting system 500 of FIG. 5, a datastream manager 410 can be configured to facilitate stream assignment andan interference manager 412 can be configured to facilitate suppressionof inter-cell interference 414 and intra-cell interference 416.

An allocation module 502 can be configured to perform stream assignmentaccording to the following:

$\begin{matrix}{\mspace{79mu}{\max\limits_{\{ d_{nj}\}}{\sum\limits_{n = 1}^{G}{\sum\limits_{j = 1}^{K}{d_{nj}.}}}}} & {{Equation}\mspace{14mu} 8} \\{{{S.t.\mspace{14mu}{\sum\limits_{\underset{g \neq n}{{{({g,k})} \in S_{U}},{{({n,j})} \in S_{V}}}}{d_{gk}d_{nj}}}} \leq {{\sum\limits_{{({n,j})} \in S_{V}}{d_{nj}\left( {N_{n}^{t} - {\sum\limits_{k = 1}^{K}d_{nk}}} \right)}} + {\sum\limits_{{({g,k})} \in S_{U}}{d_{gk}\left( {N_{gk}^{r} - d_{gk}} \right)}}}}\mspace{20mu}{{\forall S_{V}},{S_{U} \subseteq S},\mspace{20mu}{{{where}\mspace{20mu} S} = {\left\{ {{{\left( {g,k} \right)\text{:}g} \in \left\{ {1,\ldots\mspace{14mu},G} \right\}},{k \in \left\{ {1,\ldots\mspace{14mu},K} \right\}}} \right\}.}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

A first updater 504 can be configured to perform inter-cell interferencesuppression given by:

$\begin{matrix}{\min\limits_{V_{nj}^{F},U_{gk}}{\sum\limits_{\underset{\neq n}{g = 1}}^{G}{\sum\limits_{k = 1}^{K}{{{trace}\left( {\left( {U_{gk}H_{{gk},n}V_{nj}^{I}} \right)^{H}\left( {U_{gk}H_{{gk},n}V_{nj}^{I}} \right)} \right)}.}}}} & {{Equation}\mspace{14mu} 10} \\{{{S.t.\mspace{14mu} V_{nj}^{I}} = {V_{nj}^{C} + {S_{n}V_{nj}^{F}}}},{V_{nj}^{F} \in {C^{{({N_{n}^{t} - {\sum\limits_{k = 1}^{K}d_{nk}^{*}}})} \times d_{nj}^{*}}.}}} & {{Equation}\mspace{14mu} 11} \\{{{U_{gk}U_{gk}^{H}} = I},{U_{gk} \in {C^{d_{k} \times N_{gk}^{r}}.}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$∀g∈{1, . . . , G}, k∈{1, . . . , K}, where: {d*_(nj)} are solved by theallocation module 502 during the stream assignment, matrices V_(nj)^(C)∈C^(N) ^(n) ^(t) ^(×d) ^(nj) ^(*) , S_(n)∈C^(N) ^(n) ^(t) ^(×(N)^(n) ^(t) ^(−Σ) ^(k=1) ^(K) ^(d) ^(nk) ^(*) ⁾, are isometry matriceswhose row vectors combined together form a basis for C^(N) ^(n) ^(t)^(×1), for example,[V _(n1) ^(C) ,V _(n2) ^(C) , . . . ,V _(nK) ^(C) ,S _(n)]^(H) [V _(n1)^(C) ,V _(n2) ^(C) , . . . V _(nK) ^(C) ,S _(n) ]=I.  Equation 13.

With continuing reference to FIG. 5, a second updater 506 can beconfigured to perform intra-cell interference suppression, where

$\begin{matrix}{\mspace{79mu}{\min\limits_{V_{nj}}{\sum\limits_{{k = 1},{\neq j}}^{K}{{{trace}\left( {\left( {U_{nk}^{*}H_{{nk},n}V_{nj}} \right)^{H}\left( {U_{nk}^{*}H_{{nk},n}V_{nj}} \right)} \right)}.}}}} & {{Equation}\mspace{14mu} 14} \\{\mspace{79mu}{{{S.t.\mspace{14mu}\left( V_{nj} \right)^{H}}V_{nj}} = {I.}}} & {{Equation}\mspace{14mu} 15} \\{\mspace{79mu}{{{rank}\left( {U_{nj}^{*}H_{{nj},j}V_{nj}} \right)} = {d_{nj}^{*}.}}} & {{Equation}\mspace{14mu} 16} \\{{{span}_{c}\left( \left\lbrack {V_{n\; 1},V_{n\; 2},\ldots\mspace{14mu},V_{nK}} \right\rbrack \right)} \subseteq {{{span}_{c}\left( \left\lbrack {V_{n\; 1}^{I^{*}},V_{n\; 2}^{I^{*}},\ldots\mspace{14mu},V_{nK}^{I^{*}}} \right\rbrack \right)}.}} & {{Equation}\mspace{14mu} 17}\end{matrix}$where {V_(nj) ^(I*)} and {U*_(nj)}, n∈{1, . . . , G}, j∈{1, . . . , K},are the solutions obtained by the first updater 504, and span_(c) (X)denotes the linear space spanned by the row vectors of X. Furtherdetails related to the configurations of the allocation module 502, thefirst updater 504, and the second updater 506 will be provided below.

To appreciate the disclosed aspects, the following provides a connectionbetween an initial IA solution and the IA solution decomposed by theallocation module 502, the first updater 504, and the second updater506. For fully connected MIMO cellular networks with i.i.d. channelmatrices {H_(gk,n)}, the variables optimized by IA for MIMO cellularnetworks (e.g., refer to Equations 2 through 5) is given by ({d*_(gk)},{U*_(gk)}, {V*_(gk)}) with probability one (1), where {d*_(gk)};{U*_(gk)}, {V*_(gk)} are the solutions derived by the allocation module502, the first updater 504, and the second updater 506, respectively. Inaddition the optimal value of IA for MIMO cellular networks (e.g., referto Equations 2 through 5) is D*=Σ_(n=1) ^(G) Σ_(j=1) ^(K)d*_(nj).

The allocation module 502 can determine the stream assignment {d_(nj)}to maximize the sum of the data stream numbers (e.g., DoF) of thenetwork, conditioned on the network being IA feasible, which can bedetermined by an application module 510, which will be discussed below.Further, the first updater 504 can update the intermediate precoders{V_(nj) ^(I)} and decorrelators {U_(gk)} to suppress the inter-cellinterferences. The second updater 506 can further adjust the precoders{V_(nj)} to suppress the intra-cell interferences.

It is noted that after first updater 504 and second updater 506 performthe respective updates (e.g., the process of inter-cell and intra-cellinterference mitigation is separated), only inter-cell channel states{H_(gk,n)}, g≠n are involved in the process employed by the firstupdater 504. This property can be utilized to overcome thecross-link/direct link overlapping issue as discussed above.

With reference to the intermediate precoder updated by the first updater504 and the second updater 506, the structure of the intermediateprecoder will now be described. In contrast to some iterative IAalgorithms, the disclosed aspects utilize an auxiliary variable, namelythe intermediate precoder variables {V_(nj) ^(I)}. From Equation 11,V_(nj) ^(I) consists of the core space V_(nj) ^(C), the free spaceS_(n), and the free elements V_(nj) ^(F). This precoder structure in theauxiliary variable can help to enable separation of inter-cell andintra-cell interference suppression.

The physical definition of Equation 17 will now be discussed. Equation17 is introduced to assist to ensure that the desirable inter-cellinterference alignment property obtained by the first updater 504 can bemaintained during the precoder updates {V_(nj)} performed by the secondupdater 506. This is due, at least in part, to the following. Forexample, suppose {U*_(gk)} and {V_(nj) ^(I*)} constitute the solutionderived by the first updater 504. This results in U*_(gk)H_(gk,n)[V_(n1)^(I*), V_(n2) ^(I*), . . . , V_(nK) ^(I*)]=0, ∀g≠n∈{1, . . . , G}. FromEquation 17, there exists a matrix R_(n)∈C^(Σ) ^(j=1) ^(K) ^(d) ^(nj)^(×Σ) ^(j=1) ^(K) ^(d) ^(nj) such that [V_(n1), V_(n2), . . . ,V_(nK)=V_(n1) ^(I*), V_(n2) ^(I*), V_(nK) ^(I*)] R_(n), which leads tothe following equation:U* _(gk) H _(gk,n) [V _(n1) ,V _(n2) , . . . ,V _(nK) ]=U* _(gk) H_(gk,n) [V _(n1) ^(I*) ,V _(n2) ^(I*) , . . . ,V _(nK) ^(I*) ]R _(n)=0·R_(n)=0.  Equation 18.Equation 18 illustrates that the inter-cell interference alignmentproperty is preserved for the updated precoders {V_(nj)} (e.g., theprecoders updated by the second updater 506).

With continuing reference to the data stream manager 410 and theallocation module 502 of FIG. 5, the stream assignment is acombinatorial problem whose solution {d*_(gk)} can involve exhaustivesearch with exponential complexity with respect to the total number ofMSs GK. For low complexity consideration, a greedy-based solution can beutilized, according to an implementation.

For the greedy stream assignment, a policy manager 508 can be configuredto initialize a stream assignment policy (referred to as the “firststep” for purposes of explanation). For example, the stream assignmentpolicy can be initialized to be the number of streams requested by eachMS of the plurality of MSs within the network. This can be expressed as:d_(gk)=d_(gk) ^(max), ∀g∈{1, . . . , G}, k∈{1, . . . , K}.

An application module 510 can be configured to determine whether it isfeasible to use IA in the wireless network under consideration (referredto as the “second step” for purposes of explanation). For example, theapplication module 510 can be configured to perform a low complexity IAfeasibility check. In this case, v_(nj) ^(t), v_(gk) ^(r), n, g∈{1, . .. , G}, j, k∈{1, . . . , K} can be denoted as the number of freedoms.For example, the number of freedoms can be the free variables inprecoder V_(nj) ^(I) and decorrelator U_(gk),respectively. It is notedthat the number of freedoms in V_(nj) ^(I) are given by the number ofelements in V_(nj) ^(F) and that in U_(gk) are given by the dimension ofGrassmannian G(d_(gk),N_(gk) ^(r)). This results in:

$\begin{matrix}{{v_{nj}^{t} = {d_{nj}\left( {N_{g}^{t} - {\sum\limits_{k = 1}^{K}d_{nk}}} \right)}},{v_{gk}^{r} = {{d_{gk}\left( {N_{gk}^{r} - d_{gk}} \right)}.}}} & {{Equation}\mspace{14mu} 19.}\end{matrix}$where c_(gk,nj), n, g∈{1, . . . , G}, j∈{1, . . . , K}, k∈{1, . . . ,K}, is denoted as the number of constraints used to reduce (or nearlyeliminate) the interference from V_(nj) to U_(gk). Setc _(gk,nj) =d _(nj) d _(gk), if g≠n;c _(gk,nj)=0, otherwise.  Equation20.

In an implementation, a low complexity IA feasibility-checking algorithmcan be utilized by the application module 510 to determine if thenetwork can benefit from IA and/or if IA can be applied to the network.If the network is IA feasible, let d*_(gk)=d_(gk), g∈{1, . . . , G},k∈{1, . . . , K} and no further action is taken (e.g., exit thealgorithm).

If the network is not interference alignment feasible, updated_(g′k′)=d_(g′k′)−1 (referred to as the “third step” for purposes ofexplanation) and return to the second step, where (g′,k′) is given by:

$\begin{matrix}\begin{matrix}{\left( {g^{\prime},k^{\prime}} \right) = {\arg\;{\max\limits_{g,k}\begin{pmatrix}{{\sum\limits_{n = 1}^{G}{\sum\limits_{j = 1}^{K}\left( {c_{{gk},{nj}} + c_{{nj},{gk}} - c_{{gk},{nj}}^{\prime} - c_{{nj},{gk}}^{\prime}} \right)}} -} \\\left( {v_{gk}^{t} + v_{gk}^{r} - v_{gk}^{\prime\; t} - v_{gk}^{\prime\; r}} \right)\end{pmatrix}}}} \\{= {\arg\;{\max\limits_{g,k}{\left( {{2{\sum\limits_{n = 1}^{G}{\sum\limits_{\underset{{({n,j})} \neq {({g,k})}}{j = 1}}^{K}d_{nj}}}} - \left( {N_{g}^{t} + N_{gk}^{r} - {4d_{gk}} + 2} \right)} \right).}}}}\end{matrix} & {{Equation}\mspace{14mu} 21}\end{matrix}$where {v′_(gk) ^(t),v′_(gk) ^(r)}, and {c′_(gk,nj),c′_(nj,gk)} denotethe number of freedoms and constraints given by Equation 19 and Equation20, respectively, with d′_(gk)=d_(gk)=1.

For purposes of explanation, the property of the low complexity IAfeasibility checked applied by the application module 510 will bedescribed. The IA feasibility constraint in Equation 9 is satisfied if,and only, if it can satisfy a low complexity IA feasibility checking.For example purposes, a low complexity IA feasibility checking approachwill now be defined.

For notational convenience, v_(nj) ^(t), v_(gk) ^(r) and c_(gk,nj) aredenoted as v_(n) ^(t), v_(g) ^(r) and c_(gn), respectively, wheren=(n,j), g=(g,k), n, g∈{1, . . . , G}, j, k∈{1, . . . , K}.

The constraint assignment is initialed by randomly generalizing aconstraint assignment policy, such as, for example, {c_(ng) ^(t),c_(gn)^(r)} such that: c_(ng) ^(t), c_(gn) ^(r)∈N∪{0}, c_(ng) ^(t)+c_(gn)^(r)=c_(gn). Calculate {P_(n) ^(t),P_(g) ^(r)}: P_(n) ^(t)=v_(n)^(t)−Σ_(g∈s)c_(ng) ^(t), P_(g) ^(r)=v_(g) ^(r)−Σ_(n∈s)c_(gn) ^(r). Next,the constraint assignment is updated. For example, there can existoverloaded nodes (e.g., P_(n) ^(t)<0 or P_(g) ^(r)<0). In this case, thefollowing is performed to update the constraint assignment {c_(gn)^(t),c_(gn) ^(r)}.

First, is initialization wherein an overloaded node with negativepressure is selected, without losing generality (referred to as Step A).For example, assume P_(n) ^(t)<0, in this case P_(n) ^(t) is set to bethe root node of the pressure transfer tree. The pressure transfer treeis a variation of the tree data structure, with its nodes storing thepressures at the precoders and decorrelators, its link strengths storingthe maximum number of constraints that can be reallocated between theparent nodes and the child nodes.

Second, leaf nodes are added to the pressure transfer tree (referred toas Step B). For every leaf node P_(n) ^(x) (x∈{t,r}). For every g: Ifc_(ng) ^(x) >0, add P_(g) ^(x) as a child node of P_(n) ^(x) with linkstrength c_(ng) ^(x) , where x is the element in {t,r} other than x.

Next, pressure is transferred from root to leaf nodes (referred to asStep C). For every leaf node with positive pressure, transfer pressurefrom root to these leafs by updating the constraint assignment policy{c_(gn) ^(t),c_(gn) ^(r)}. For example,

$P_{n_{1}}^{t}\overset{c_{n_{1}g_{1}}^{t}}{\longrightarrow}P_{g_{1}}^{r}\overset{c_{g_{1}n_{2}}^{r}}{\longrightarrow}P_{n_{2}}^{t}$is a root-to-leaf branch of the tree. Update: (c_(n) ₁ _(g) ₁^(t))′=c_(n) ₁ _(g) ₁ ^(t)−ε, (c_(g) ₁ _(n) ₁ ^(r))′=c_(g) ₁ _(n) ₁ +ε,(c_(g) ₁ _(n) ₂ )′=c_(g) ₁ _(n) ₂ ^(r)−ε, (c_(n) ₂ _(g) ₁ ^(t))′=c_(n) ₂_(g) ₁ ^(t)+ε. This results in (P_(n) ₁ ^(t))′=P_(n) ₁ ^(t)−ε and (P_(n)₂ ^(t))′=P_(n) ₂ ^(t)+ε, where ε=min (−P_(n) ₁ ^(t),P_(n) ₂ ^(t),c_(n) ₁_(g) ₁ ^(t),c_(g) ₁ _(n) ₂ ^(r)).

Next, the depleted links and neutralized roots are removed (referred toas Step D). For example, if the strength of a link becomes zero (0)after the pressure is transferred as described above, separate thesubtree rooted from the child node of this link from the originalpressure transfer. In another example, if the root of a pressuretransfer tree is nonnegative, remove the root and, therefore, thesubtrees rooted from each child node of the root become new trees. Thisprocess is repeated until all roots are negative. For each newlygenerated pressure transfer tree, Steps B through D are repeated.

Conditions are exited (referred to as Step E). Steps A through D arerepeated until all trees become empty (e.g., the network is IA feasible)or no new leaf node can be added for any of the non-empty trees in StepB (e.g., the network is IA infeasible). Exit the algorithm.

The worst-case complexity of the above described checking scheme isO(G³K³), which is substantially lower compared with the complexityO(2^(G) ² ^(K) ² ) in some IA feasibility checking techniques.

With continuing reference to FIG. 5, the first updater 504 can beconfigured to alternatively update the intermediate precoders {V_(nj)^(I)} and the decorrelators {U_(gk)}. The updating by the first updater504 can be performed to minimize the inter-cell interference 414. Forexample,

$\begin{matrix}{{\min\limits_{V_{nj}^{F}}{\sum\limits_{\underset{\neq n}{g = 1}}^{G}{\sum\limits_{k = 1}^{K}{{trace}\left( {\left( {U_{gk}H_{{gk},n}V_{nj}^{I}} \right)^{H}\left( {U_{gk}H_{{gk},n}V_{nj}^{I}} \right)} \right)}}}},{{S.t.\text{:}}\mspace{14mu}{equation}\mspace{14mu}(11)},} & {{Equation}\mspace{14mu} 22.} \\{{\min\limits_{U_{gk}}{\sum\limits_{\underset{\neq n}{g = 1}}^{G}{\sum\limits_{k = 1}^{K}{{trace}\left( {\left( {U_{gk}H_{{gk},n}V_{nj}^{I}} \right)^{H}\left( {U_{gk}H_{{gk},n}V_{nj}^{I}} \right)} \right)}}}},{{S.t.\text{:}}\mspace{14mu}{equation}\mspace{14mu}{(12).}}} & {{Equation}\mspace{14mu} 23.}\end{matrix}$

According to an alternative implementation for intra-cell interferencesuppression, the following is provided. Initialization can occur byrandomly generating V_(nj) ^(F), ∀n∈{1, . . . , G}, j∈{1, . . . , K}(referred to as step 1A for purposes of this description). Next,interference leakage can be minimized at the receiver side (referred toas step 2A for purposes of this description). For example, at the k-thMS of BS-g update U_(gk): u_(gk)(d)=(v_(d)[Σ_(n=1,≠g) ^(G)Σ_(j=1)^(K)P_(nj)(H_(gk,n)V_(nj) ^(I))(H_(gk,n)V_(nj) ^(I))^(H)])^(H), whereu_(gk)(d) is the d-th row of U_(gk), v_(d)[A] is the eigenvectorcorresponding to the d-th smallest eigenvalue of A, d∈{1, . . .,d_(gk)}.

Further to this alternative implementation, interference leakage at thetransmitter side can be minimized (referred to as step 3A for purposesof this detailed description). For example, at BS-n, update V_(nj) ^(F),j∈{1, . . . , K}: V_(nj) ^(F)=−(S_(n) ^(H)Q_(nj)S_(n))⁻¹S_(n)^(H)Q_(nj)V_(nj) ^(C), where Q_(nj)=Σ_(g=1,≠n) ^(G)Σ_(k=1)^(K)P_(nj)(U_(gk) ^(H)H_(gk,n))^(H)(U_(gk)H_(gk,n)).

Steps 2A and 3A, described above, can be repeated until V_(nj) ^(F) andU_(gk) converges. Set V_(nj) ^(I*)=V_(nj) ^(C)+S_(n)V_(nj) ^(F) andU*_(gk)=U_(gk).

For fully connected MIMO cellular network with i.i.d. channel matrices{H_(gk,n)}, the alternative implementation described above converges toa local optimal solution as derived by the second updater 506. It shouldbe noted, however, that global optimality might not be achieved, nor isit guaranteed.

The following discusses the rank property of the conversed solution ofthe above noted alternative implementation in the direct links. As itrelates to the property of [V_(nj) ^(I*)] and [U*_(nj)]), for a fullyconnected MIMO cellular network with i.i.d. channel matrices {H_(gk,n)},the converged solution of the alternative intra-cell interferencesuppression discussed above, {V_(nj) ^(I*)}, U*_(nj), n∈{1, . . . , G},j∈{1, . . . , K} satisfy

$\begin{matrix}{{{{rank}\left( {\begin{bmatrix}{\left( U_{n\; 1}^{*} \right)^{H}H_{{n\; 1},n}} \\{\left( U_{n\; 2}^{*} \right)^{H}H_{{n\; 2},n}} \\\ldots \\{\left( U_{nK}^{*} \right)^{H}H_{{nK},n}}\end{bmatrix}\left\lbrack {V_{n\; 1}^{I^{*}},V_{n\; 2}^{I^{*}},\ldots\mspace{14mu},V_{nK}^{I^{*}}} \right\rbrack} \right)} = {\sum\limits_{j = 1}^{K}d_{nj}}},\mspace{20mu}{\forall{n \in \left\{ {1,\ldots\mspace{14mu},G} \right\}}}} & {{{Equation}\mspace{11mu} 24.}\;}\end{matrix}$

With continuing reference to FIG. 5, the second updater 506 can performintra-cell interference suppression through utilization of the followingconstructive algorithm, referred to as intra-cell zero forcing. Denote W_(q)=[W₁ ^(H), . . . , W_(q−1) ^(H), W_(q+1) ^(H), . . . , W_(K) ^(H),W_(q) ^(H)]^(H), where W_(q)=(U*_(nq))H_(nq,n), q∈{1, . . . , K}. EachBS can perform the following for every q∈{1, . . . , K} to calculate theprecoders. At a first step, LQ decomposition is performed for W_(q)[V_(n1) ^(I*), V_(n2) ^(I*), . . . , V_(nK) ^(I*)]=L_(n)(q)Q_(n)(q),where Q_(n)(q) is an Σ_(j=1) ^(K)d_(nj)×Σ_(j=1) ^(K)d_(nj) unitarymatrix, and L_(n)(q) is a Σ_(j=1) ^(K)d_(nj)×Σ_(j=1) ^(K)d_(nj), lowertriangular matrix.

At a second step, set V′_(nq)=[V_(n1) ^(I*), V_(n2) ^(I*), . . . ,V_(nK) ^(I*)]Q′_(n)(q), where Q′_(n)(q) is a matrix aggregated by thelast d_(nq) columns of Q_(n) ^(H)(q). At a third step, singular valuedecomposition is performed for V′_(nq)=A_(nq)S_(nq)B_(nq) ^(H), whereS_(nq) is a N_(g) ^(t)×d_(nq) matrix, A_(nq) and B_(nq) are N_(g)^(t)×N_(g) ^(t) and d_(nq)×d_(nq) matrices, respectively. SetV*_(nq)=A′_(nq), where A′_(nq) is a matrix aggregated by the firstd_(nq) columns of A_(nq).

Another aspect relates to optimizing {V*_(nj)} for fully connected MIMOcellular networks with i.i.d. channel matrices {H_(gk,n)}, the output ofthe intra-cell zero-forcing {V*_(nj)}, n∈{1, . . . , G}, j∈{1, . . .,K}, can be the best solution derived by the second updater 506 (e.g.,with optimal value (intra-cell interference power)=0).

As it relates to MIMO cellular networks with partial connectivity, therecan be space restriction on transceivers. For example, in point-to-pointMIMO or single BS MIMO cellular networks, partial connectivity can beharmful to system performance. However, as discussed herein, partialconnectivity can be beneficial to system performance in MIMOinterference networks since partial connectivity provides an extradimension of freedom, namely the interference nulling to eliminateinterference. For example, by restricting transceivers to lowerdimensional subspaces in partially connected MIMO interference networks,many IA constraints can be eliminated (or substantially reduced) at acost of only a few freedoms in transceiver design and, therefore, the IAfeasibility region is extended.

In an example, the subspace constraint can be extended to exploit thepartial connectivity in MIMO networks and a transceiver structure willbe described. Provided is an intermediate precoder with dynamic freespace: V_(nj) ^(I)=V_(nj) ^(C)+S_(nj) ^(t)V_(nj) ^(F), and adecorrelator with dynamic linear filter:

U_(nj)=U_(nj) ^(F)S_(nj) ^(r), where S_(nj) ^(t)∈C^(N) ^(n) ^(t) ^(×s)^(nj) ^(t) , V_(nj) ^(F)∈C^(S) ^(nj) ^(t) ^(×d) ^(nj) , S_(nj)^(r)∈C^((d) ^(nj) ^(+s) ^(nj) ^(r) ^()×N) ^(nj) ^(r), U_(nj) ^(F)∈C^(d)^(nj) ^(×(d) ^(nj) ^(+s) ^(nj) ^(r) ⁾, S_(nj) ^(t)∈{0, 1, . . . N_(n)^(t)−Σ_(k=1) ^(K)d_(nj)}, S_(nj) ^(r)∈{0, 1, . . . N_(nj) ^(r)−d_(nj)}.

There can also be a space restriction via new transceiver structures. Itis noted that span_(c)(V_(nj) ^(t))⊂cspan_(c)(V_(nj)^(C))+span_(c)(S_(nj) ^(t)), and span_(r)(U_(nj))⊂span_(r)(S_(nj) ^(r)),space restriction is imposed on V_(nj) ^(I) and U_(nj) by the newtransceiver structure. As a special case, when S_(nj) ^(t)=N_(n)^(t)−Σ_(k=1) ^(K)d_(nj), S_(nj) ^(r)=N_(nj) ^(r)−d_(nj), the transceiverstructure is reduced as compared to the transceiver structure describedabove.

As it relates to MIMO cellular networks with partial connectivity, theIA for MIMO Cellular Networks (e.g., Equations 2 through 5), can bedecomposed into three sections. The data stream assignment is modifiedas per the following.

For the stream assignment and subspaces design,

$\begin{matrix}{\mspace{79mu}{\max\limits_{{\{ d_{nj}\}},{\{ V_{nj}^{C}\}},{\{ S_{nj}^{t}\}},{\{ S_{nj}^{r}\}}}{\sum\limits_{n = 1}^{G}{\sum\limits_{j = 1}^{K}{d_{nj}.}}}}} & {{Equation}\mspace{14mu} 25} \\{{{{S.t.\mspace{14mu}{\sum\limits_{\underset{{{({n,j})} \in S_{V}},{g \neq n}}{{{({g,k})} \in S_{U}},}}{{\min\left( d_{gk} \middle| {{{span}_{r}\left( S_{gk}^{r} \right)}\bigcap\left( {N^{\prime}\left( H_{{gk},n} \right)} \right)^{\bot}} \right)}{\min\left( d_{nj} \middle| {{{span}_{c}\left( V_{nj}^{C} \right)} + {{span}_{c}\left( V_{nj}^{t} \right)}} \right)}}}}\bigcap\left( {N^{\prime}\left( H_{{gk},n} \right)} \right)^{\bot}} \leq {{\sum\limits_{{({n,j})} \in {Sv}}{d_{nj}S_{nj}^{t}}} + {\sum\limits_{{({g,k})} \in {Su}}{d_{gk}S_{nj}^{r}}}}},\mspace{20mu}{\forall S_{V}},{S_{U} \subseteq S},\mspace{79mu}{{{where}\mspace{14mu} S} = {\left\{ {{{\left( {g,k} \right)\text{:}g} \in \left\{ {1,\ldots\mspace{14mu},G} \right\}},{k \in \left\{ {1,\ldots\mspace{14mu},K} \right\}}} \right\}.}}} & {{Equation}\mspace{14mu} 26} \\{{{\left\lbrack {V_{n\; 1}^{C},V_{n\; 2}^{C},\ldots\mspace{14mu},V_{nK}^{C},S_{nj}^{t}} \right\rbrack^{H}\left\lbrack {V_{n\; 1}^{C},V_{n\; 2}^{C},\ldots\mspace{14mu},V_{nK}^{C},S_{nj}^{t}} \right\rbrack} = I},\mspace{79mu}{V_{nj}^{C} \in \left( {N\left( H_{{nj},n} \right)} \right)^{\bot}},} & {{Equation}\mspace{14mu} 27.} \\{\mspace{79mu}{{{S_{nj}^{r}\left( S_{nj}^{r} \right)}^{H} = I},{S_{nj}^{r} \in \left( {N^{\prime}\left( H_{{nj},n} \right)} \right)^{\bot}},\mspace{79mu}{\forall{n \in \left\{ {1,\ldots\mspace{14mu},G} \right\}}},{j \in {\left\{ {1,\ldots\mspace{14mu},K} \right\}.}}}} & {{Equation}\mspace{14mu} 28.}\end{matrix}$

As it relates to the suppression performed by the first updater 504 andthe second updater 506 for a MIMO network with partial connectivity, theequations are substantially the same except that, V_(nj) ^(C), S_(n),and U_(nj) are replaced with V_(nj) ^(C*), S_(nj) ^(T*), and U_(nj)^(F)S_(nj) ^(R*), respectively, where {V_(nj) ^(C*)}, {S_(nj) ^(T*)},and {S_(nj) ^(R*)} are the solutions to the above stream assignment andsubspaces design (e.g., Equations 25 through 28).

To appreciate the disclosed aspects, the following provides a connectionbetween an initial IA solution and the IA solution decomposed by theallocation module 502, the first updater 504, and the second updater 506as it relates to a partially connected MIMO networks. For partiallyconnected MIMO cellular networks, with probability 1, the solutions ofthe stream assignment and subspaces design determination and theinterference suppressions, for example, {d*_(gk)}, {U*_(gk)}, {V*_(gk)},are also a valid solution of the IA for MIMO cellular networks (e.g.,Equations 2 through 5). Therefore, the performance of the decomposedproblems, for example, Σ_(g=1) ^(G)Σ_(k=1) ^(K)d*_(gk) gives a lowerbound of that of the original problem.

In an implementation, the greedy-based algorithm can be extended to thepartial connectivity situation, which is now described with reference toSteps 1 through 6. In this case, at Step 1, the number of streams isinitialized as d_(nj)=min(rank(H_(nj,n)), d_(nj) ^(max)), ∀n∈{1, . . . ,G}, j∈{1, . . . , K}.

At Step 2, the common null spaces are calculated. At each BS n∈{1, . . ., G}, calculate the intersection of the null spaces of the inter-cellcross links, for example, N_(n)(M)=∩_((g,k)∈M)N(H_(gk,n)), M⊂{(g,k):g≠n∈{1, . . . , G}, k∈{1, . . . , K}}, as follows:

First, denote M_(n)={(g,k):H_(nm)≠0}. Initialize N_(n)(Ø)=C^(N) ^(n)^(t) , N_(n)({(g,k)})=N_(n)(H_(gk,n)), and set the cardinality parameterC=2.

Second, for every M⊂M_(n) with |M|=C, if all the subsets of M withcardinality (C−1) are not {0}, calculateN_(n)(M)=N_(n)(M\{(g′,k′)})∩N({(g′,k′}), where (g′, k′) is an arbitraryelement in K_(sub). Update C=C+1. Repeat this process until N(M)={0},∀M⊂M_(n) with |M|=C or C=|M_(n)|.

Third, for every M⊂M_(n) with N_(n) (M)≠{0}, set N_(n)(M∪({1, . . . ,K}\M_(n)))=N_(n)(M)

Then, at each MS M_(gk), calculate N_(gk) ^(r)(M′)=∩_(n∈M′)N(H_(gk,n)),M′⊂{n:n≠g∈{1, . . . , G}} using a similar process.

At Step 3, Design V_(nj) ^(C) (e.g., span_(c)(V_(nj) ^(C))): At BS n,n∈{1, . . . , G}, design V_(nj) ^(C), j∈{1, . . . , K} one by one asfollows: For the j-th MS of BS-n,

First, update the number of streams assigned to the j-th MS of BS-n ifthere is not enough signal dimension left, for example, updated_(nj)=min(d_(nj),N_(g) ^(t)−dim((+_(k<J)V_(nk) ^(C))+N(H_(nj))));

Then, design V_(nj) ^(C) based on the principles that A) V_(nj) ^(C) isorthogonal to the previous designed core spaces and is contained by theeffective subspace of the direct link, for example, V_(nj) ^(C)⊂((+_(k<j)V_(nk) ^(C))+N(H_(nj)))^(⊥); B) A subspace which belongs to anull space N (M) with larger weight (e.g., W_(n)(N (M)), defined below)is selected with higher priority.

$\begin{matrix}{{W_{n}\left( {N(M)} \right)} = {\sum\limits_{{({g,k})} \in M}{{\min\left( {d_{gk},{{rank}\left( H_{{gk},n} \right)}} \right)}.}}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

From the left side of Equation 26, this weight is the maximum number ofIA constraints that can be mitigated by selecting a one dimensionalsubspace in N (M).

At Step 4, Design S_(nj) ^(t and S) _(gk) ^(r) (e.g., span_(c)(S_(nj)^(t)), span_(r)(S_(gk) ^(r))):

At BS n, n∈{1, . . . , G}, design {S_(nj) ^(t)}:

A. Generate a series of potential S_(nj) ^(t)(d), d∈{0, 1, . . . , N_(g)^(t)−Σ_(k=1) ^(K)d_(nk)} with dim(S_(nj) ^(t)(d))=d based on theprinciples that A) S_(nj) ^(t) ⊂((+_(k∈{1, . . . , K})V_(nk) ^(C)))^(⊥),B). Similar to the principle B in Step 3.

B. Choose the best possible S_(nj) ^(t): Set S_(nj) ^(t)=S_(nj)^(t)(d*), where

$\begin{matrix}{d^{*} = {\arg\;{\max\limits_{d}{\begin{pmatrix}{d_{nj}{d--}{\sum\limits_{{g = 1},{\neq n}}^{G}{\sum\limits_{k = 1}^{K}{\min\;\left( {d_{gk},{{rank}\left( H_{{gk},n} \right)}} \right) \times}}}} \\{{\min\left( {d_{nj},{{\left( {V_{nj}^{C} + {S_{nj}^{t}(d)}} \right)\bigcap\left( N_{{gk},n}^{t} \right)^{\bot}}}} \right)} -}\end{pmatrix}.}}}} & {{Equation}\mspace{14mu} 30.}\end{matrix}$

In a similar manner, at each MS M_(gk), generate S_(nj) ^(r)(d), d∈{0,1, . . . , N_(gk) ^(r)−d_(gk)} based on principle B. Set S_(gk)^(r)=S_(gk) ^(r)(d*), where

$\begin{matrix}{d^{*} = {\arg\;{\max\limits_{d}{\begin{pmatrix}{d_{gk}{d--}{\sum\limits_{{n = 1},{\neq g}}^{G}{\sum\limits_{j = 1}^{K}{\min\;\left( {d_{gk},{{S_{gk}^{r}\bigcap\left( N_{{gk},n}^{r} \right)^{\bot}}}} \right) \times}}}} \\{{\min\left( {d_{nj},{{\left( {V_{nj}^{C} + {S_{nj}^{t}(d)}} \right)\bigcap{N\left( H_{{gk},n} \right)}^{\bot}}}} \right)} -}\end{pmatrix}.}}}} & {{Equation}\mspace{14mu} 31.}\end{matrix}$

Feasibility checking is performed at Step 5. In this case, set v_(nj)^(t)=d_(nj)S_(nj) ^(t), v_(gk) ^(r)=d_(gk)S_(gk) ^(r), where S_(nj) ^(t)and S_(gk) ^(r) are defined above with respect to the transceiverstructure to exploit partial connectivity. Setc_(gk,nj)=min(d_(gk),|span_(r)(S_(gk)^(r))∩N(H_(gk,n))^(⊥)|)min(d_(nj),|(span_(c)(V_(nj)^(C))+span_(c)(S_(nj) ^(t)))∩N(H_(gk,n))^(⊥)|), if g≠n; C_(gk,nj)=0,otherwise. Use a low complexity algorithm to check if the network is IAfeasible (e.g., the low complexity algorithm discussed above). If thenetwork is not IA feasible, go to Step 6. Otherwise, set d*_(nj)=d_(nj),and set V_(nj) ^(C*), S_(nj) ^(t*), S_(nj) ^(r*) to be matricesaggregated by the basis vectors of V_(nj) ^(C) and S^(t) _(nj), S^(r)_(nj), respectively, ∀n∈{1, . . . , G}, j∈{1, . . . , K}. Exit thealgorithm.

At Step 6, the stream assignment is updated. Updated=d_(g′k′)=d_(g′k′)−1 and go back to Step 2, where (g′,k′) is given by(the first line of) Equation 21.

As it relates to the subspace design criterion in the above greedy-basedsolution for the partially connected case, similar to the streamassignment criteria (e.g., Equation 21), the core space {V_(nj) ^(C)}and free space {S_(nj) ^(t)} should be designed to alleviate the IAfeasibility constraint as much as possible in order to enhance thenetwork DoF. Therefore, both Equation 29 and Equation 30 can be designedto maximize the difference between the number of freedoms inintermediate precoder design minus the number of inter-cell IAconstraints.

In an example, the above described greedy-based solution for thepartially connected case is a backward compatible extension of thegreedy stream assignment discussed earlier in this detailed description.When the network is fully connected (e.g., Steps 2 to 4 in the partiallyconnected greedy-based solution), {V_(nj) ^(C)}, {S_(nj) ^(t)}, and{S_(nj) ^(r)} will be generated with S_(nj) ^(t)=S_(n), ∀j∈{1, . . . ,K}} and rank(S_(nj) ^(r))=N_(nj) ^(r). However, according to an aspect,this particular choice of the core space might not offer any additionalDoF gain compared to other choices of {V_(nj) ^(I)} and {S_(n)}satisfying constraint (e.g., Equation 13) in the fully connected case.

To avoid redundancy, the solutions to the interference suppressionalgorithms are similar to those discussed above with respect to thefully connected case and, therefore, will not be repeated.

According to an implementation, partial connectivity can be determinedas follows. If the channel gain of an eigenchannel is below asufficiently small threshold, the channel gain can be quantized as zeroand the channel can be defined as partially connected. For example, themaximum transmit power of BSs is P_(max) and the power of the Gaussiannoise is σ. Set the threshold to be

$\rho = {\frac{\sigma}{10\; P_{\max}}.}$When the gain of the eigenchannel g≤ρ, the power of interference on thischannel is no more than

${{\rho\; P_{\max}} = \frac{\sigma}{10\;}},$which is negligible compared to the Gaussian noise. Therefore, g can bequantized to be zero (0) and the eigenchannel can be defined aspartially connected.

In view of the example systems shown and described herein, methods thatmay be implemented in accordance with the one or more of the disclosedaspects, will be better understood with reference to the following flowcharts. While, for purposes of simplicity of explanation, the methodsare shown and described as a series of blocks, it is to be understoodthat the disclosed aspects are not limited by the number or order ofblocks, as some blocks may occur in different orders and/or atsubstantially the same time with other blocks from what is depicted anddescribed herein. Moreover, not all illustrated blocks may be requiredto implement the methods described hereinafter. It is noted that thefunctionality associated with the blocks may be implemented by software,hardware, a combination thereof or any other suitable means (e.g.device, system, process, component). Additionally, it is also noted thatthe methods disclosed hereinafter and throughout this specification arecapable of being stored on an article of manufacture to facilitatetransporting and transferring such methodologies to various devices.Those skilled in the art will understand that a method couldalternatively be represented as a series of interrelated states orevents, such as in a state diagram. The various methods disclosed hereincan be performed by a system comprising at least one processor.

FIG. 6 is an example, non-limiting method 600 for interference alignmentof partially connected MIMO cellular networks, according to an aspect.At 602, assignments for data streams transmitted by one or more devicesin a multiple-input multiple-output network are determined Determiningthe assignments can include maximizing a sum of a function of the datastreams of the MIMO network. In an implementation, the MIMO networkcomprises three or more cells.

At 604, inter-cell interference is suppressed. Further, at 606,intra-cell interference is suppressed. For example, suppressinginter-cell interference comprises updating intermediate precoders anddecorrelators and the suppressing intra-cell interference comprisesfurther adjusting the intermediate precoders.

FIG. 7 illustrates an example, non-limiting embodiment of a method 700for mitigation of interference in a communications network. At 702, aninterference alignment status of a set of communication links of acommunications network is evaluated. The set of communication links caninclude defined communication links and undefined communication links.The undefined communication links are undesired communication links(e.g., inter-cell links). The defined communication links are desiredcommunication links (e.g., intra-cell links). At 704, the definedcommunication links are distinguished from the undefined communicationlinks.

According to an implementation, the communications network is amultiple-input multiple-output communications network comprising anarbitrary number of cells, users, and antennas. In an example, thecommunications network can comprise three or more cells, however, thedisclosed aspects are not limited to this implementation.

In accordance with an implementation, the evaluating can includedetermining a network device of the communications network is configuredto operate with the application of interference alignment (e.g., IAfeasibility). According to another implementation, the evaluating caninclude determining assignments for a first set of data streams of theundefined communication links and a second set of data streams of thedefined communication links. Further to this implementation, the methodcan include maximizing a degree of freedom of a network device of thecommunications network.

At 706, a first interference caused by the defined communication linksis suppressed. In an implementation, suppressing the first interferencecaused by the defined communication links comprises suppressing thefirst interference on a per cell basis. A second interference caused bythe undefined communication links is suppressed, at 708. The secondinterference is different from the first interference. In accordancewith an implementation, suppressing the first interference can includeupdating intermediate precoders and decorrelators and suppressing thesecond interference can include adjusting the intermediate precodersafter the updating (e.g., a second adjustment).

In accordance with some aspects, the method includes initializing astream assignment policy comprising setting the stream assignment policyto be a number of streams requested by each mobile device communicatingin the network devices of the communications network. Further to thisaspect, the method includes determining a practicability of interferencealignment within the communications network. According to animplementation, the method can also include concurrently zero forcingthe first interference and the second interference.

By way of further description with respect to one or more non-limitingways to facilitate interference mitigation in partially connected MIMOnetworks, FIG. 8 is a schematic example communications environment 800that can operate in accordance with aspects described herein. Inparticular, example wireless environment 800 illustrates a set ofwireless network macro cells. Three coverage macro cells 802, 804, and806 include the illustrative wireless environment; however, it is notedthat wireless cellular network deployments can encompass any number ofmacro cells. Coverage macro cells 802, 804, and 806 are illustrated ashexagons; however, coverage cells can adopt other geometries generallydictated by a deployment configuration or floor plan, geographic areasto be covered, and so on. Each macro cell 802, 804, and 806 issectorized in a 2π/3 configuration in which each macro cell includesthree sectors, demarcated with dashed lines in FIG. 8. It is noted thatother sectorizations are possible, and aspects or features of thedisclosed subject matter can be exploited regardless of type ofsectorization. Macro cells 802, 804, and 806 are served respectivelythrough base stations or eNodeBs 808, 810, and 812. Any two eNodeBs canbe considered an eNodeB site pair. It is noted that radio component(s)are functionally coupled through links such as cables (e.g., RF andmicrowave coaxial lines), ports, switches, connectors, and the like, toa set of one or more antennas that transmit and receive wireless signals(not illustrated). It is noted that a radio network controller (notshown), which can be a part of mobile network platform(s) 814, and setof base stations (e.g., eNode B 808, 810, and 812) that serve a set ofmacro cells; electronic circuitry or components associated with the basestations in the set of base stations; a set of respective wireless links(e.g., links 816, 818, and 820) operated in accordance to a radiotechnology through the base stations, form a macro radio access network.It is further noted that, based on network features, the radiocontroller can be distributed among the set of base stations orassociated radio equipment. In an aspect, for universal mobiletelecommunication system-based networks, wireless links 816, 818, and820 embody a Uu interface (universal mobile telecommunication system AirInterface).

Mobile network platform(s) 814 facilitates circuit switched-based (e.g.,voice and data) and packet-switched (e.g., Internet protocol, framerelay, or asynchronous transfer mode) traffic and signaling generation,as well as delivery and reception for networked telecommunication, inaccordance with various radio technologies for disparate markets.Telecommunication is based at least in part on standardized protocolsfor communication determined by a radio technology utilized forcommunication. In addition, telecommunication can exploit variousfrequency bands, or carriers, which include any electromagneticfrequency bands licensed by the service provider network 822 (e.g.,personal communication services, advanced wireless services, generalwireless communications service, and so forth), and any unlicensedfrequency bands currently available for telecommunication (e.g., the 2.4GHz industrial, medical and scientific band or one or more of the 5 GHzset of bands). In addition, mobile network platform(s) 814 can controland manage base stations 808, 810, and 812 and radio component(s)associated thereof, in disparate macro cells 802, 804, and 806 by wayof, for example, a wireless network management component (e.g., radionetwork controller(s), cellular gateway node(s), etc.) Moreover,wireless network platform(s) can integrate disparate networks (e.g.,Wi-Fi network(s), femto cell network(s), broadband network(s), servicenetwork(s), enterprise network(s), and so on). In cellular wirelesstechnologies (e.g., third generation partnership project universalmobile telecommunication system, global system for mobile communication,mobile network platform 814 can be embodied in the service providernetwork 822.

In addition, wireless backhaul link(s) 824 can include wired linkcomponents such as T1/E1 phone line; T3/DS3 line, a digital subscriberline either synchronous or asynchronous; an asymmetric digitalsubscriber line; an optical fiber backbone; a coaxial cable, etc.; andwireless link components such as line-of-sight or non-line-of-sightlinks which can include terrestrial air-interfaces or deep space links(e.g., satellite communication links for navigation). In an aspect, foruniversal mobile telecommunication system-based networks, wirelessbackhaul link(s) 824 embodies IuB interface.

It is noted that while exemplary wireless environment 800 is illustratedfor macro cells and macro base stations, aspects, features andadvantages of the disclosed subject matter can be implemented in microcells, pico cells, femto cells, or the like, wherein base stations areembodied in home-based equipment related to access to a network.

To provide further context for various aspects of the disclosed subjectmatter, FIG. 9 illustrates a block diagram of an embodiment of accessequipment and/or software 900 related to access of a network (e.g., basestation, wireless access point, femtocell access point, and so forth)that can enable and/or exploit features or aspects of the disclosedaspects.

Access equipment and/or software 900 related to access of a network canreceive and transmit signal(s) from and to wireless devices, wirelessports, wireless routers, etc. through segments 902 ₁-902 _(B) (B is apositive integer). Segments 902 ₁-902 _(B) can be internal and/orexternal to access equipment and/or software 900 related to access of anetwork, and can be controlled by a monitor component 904 and an antennacomponent 906. Monitor component 904 and antenna component 906 cancouple to communication platform 908, which can include electroniccomponents and associated circuitry that provide for processing andmanipulation of received signal(s) and other signal(s) to betransmitted.

In an aspect, communication platform 908 includes a receiver/transmitter910 that can convert analog signals to digital signals upon reception ofthe analog signals, and can convert digital signals to analog signalsupon transmission. In addition, receiver/transmitter 910 can divide asingle data stream into multiple, parallel data streams, or perform thereciprocal operation. Coupled to receiver/transmitter 910 can be amultiplexer/demultiplexer 912 that can facilitate manipulation ofsignals in time and frequency space. Multiplexer/demultiplexer 912 canmultiplex information (data/traffic and control/signaling) according tovarious multiplexing schemes such as time division multiplexing,frequency division multiplexing, orthogonal frequency divisionmultiplexing, code division multiplexing, space division multiplexing.In addition, multiplexer/demultiplexer component 912 can scramble andspread information (e.g., codes, according to substantially any codeknown in the art, such as Hadamard-Walsh codes, Baker codes, Kasamicodes, polyphase codes, and so forth).

A modulator/demodulator 914 is also a part of communication platform908, and can modulate information according to multiple modulationtechniques, such as frequency modulation, amplitude modulation (e.g.,M-ary quadrature amplitude modulation, with M a positive integer);phase-shift keying; and so forth).

Access equipment and/or software 900 related to access of a network alsoincludes a processor 916 configured to confer, at least in part,functionality to substantially any electronic component in accessequipment and/or software 900. In particular, processor 916 canfacilitate configuration of access equipment and/or software 900through, for example, monitor component 904, antenna component 906, andone or more components therein. Additionally, access equipment and/orsoftware 900 can include display interface 918, which can displayfunctions that control functionality of access equipment and/or software900, or reveal operation conditions thereof. In addition, displayinterface 918 can include a screen to convey information to an end user.In an aspect, display interface 918 can be a liquid crystal display, aplasma panel, a monolithic thin-film based electrochromic display, andso on. Moreover, display interface 918 can include a component (e.g.,speaker) that facilitates communication of aural indicia, which can alsobe employed in connection with messages that convey operationalinstructions to an end user. Display interface 918 can also facilitatedata entry (e.g., through a linked keypad or through touch gestures),which can cause access equipment and/or software 900 to receive externalcommands (e.g., restart operation).

Broadband network interface 920 facilitates connection of accessequipment and/or software 900 to a service provider network (not shown)that can include one or more cellular technologies (e.g., thirdgeneration partnership project universal mobile telecommunicationsystem, global system for mobile communication, and so on) throughbackhaul link(s) (not shown), which enable incoming and outgoing dataflow. Broadband network interface 920 can be internal or external toaccess equipment and/or software 900, and can utilize display interface918 for end-user interaction and status information delivery.

Processor 916 can be functionally connected to communication platform908 and can facilitate operations on data (e.g., symbols, bits, orchips) for multiplexing/demultiplexing, such as effecting direct andinverse fast Fourier transforms, selection of modulation rates,selection of data packet formats, inter-packet times, and so on.Moreover, processor 916 can be functionally connected, through data,system, or an address bus 922, to display interface 918 and broadbandnetwork interface 920, to confer, at least in part, functionality toeach of such components.

In access equipment and/or software 900, memory 924 can retain locationand/or coverage area (e.g., macro sector, identifier(s)), access list(s)that authorize access to wireless coverage through access equipmentand/or software 900, sector intelligence that can include ranking ofcoverage areas in the wireless environment of access equipment and/orsoftware 900, radio link quality and strength associated therewith, orthe like. Memory 924 also can store data structures, code instructionsand program modules, system or device information, code sequences forscrambling, spreading and pilot transmission, access pointconfiguration, and so on. Processor 916 can be coupled (e.g., through amemory bus), to memory 924 in order to store and retrieve informationused to operate and/or confer functionality to the components, platform,and interface that reside within access equipment and/or software 900.

As it employed in the subject specification, the term “processor” canrefer to substantially any computing processing unit or deviceincluding, but not limited to including, single-core processors;single-processors with software multithread execution capability;multi-core processors; multi-core processors with software multithreadexecution capability; multi-core processors with hardware multithreadtechnology; parallel platforms; and parallel platforms with distributedshared memory. Additionally, a processor can refer to an integratedcircuit, an application specific integrated circuit, a digital signalprocessor, a field programmable gate array, a programmable logiccontroller, a complex programmable logic device, a discrete gate ortransistor logic, discrete hardware components, or any combinationthereof designed to perform the functions and/or processes describedherein. Processors can exploit nano-scale architectures such as, but notlimited to, molecular and quantum-dot based transistors, switches andgates, in order to optimize space usage or enhance performance of mobiledevices. A processor may also be implemented as a combination ofcomputing processing units.

In the subject specification, terms such as “store,” “data store,” datastorage,” “database,” and substantially any other information storagecomponent relevant to operation and functionality of a component and/orprocess, refer to “memory components,” or entities embodied in a“memory,” or components including the memory. It is noted that thememory components described herein can be either volatile memory ornonvolatile memory, or can include both volatile and nonvolatile memory.

By way of illustration, and not limitation, nonvolatile memory, forexample, can be included in memory 924, non-volatile memory (see below),disk storage (see below), and memory storage (see below). Further,nonvolatile memory can be included in read only memory, programmableread only memory, electrically programmable read only memory,electrically erasable programmable read only memory, or flash memory.Volatile memory can include random access memory, which acts as externalcache memory. By way of illustration and not limitation, random accessmemory is available in many forms such as synchronous random accessmemory, dynamic random access memory, synchronous dynamic random accessmemory, double data rate synchronous dynamic random access memory,enhanced synchronous dynamic random access memory, Synchlink dynamicrandom access memory, and direct Rambus random access memory.Additionally, the disclosed memory components of systems or methodsherein are intended to include, without being limited to including,these and any other suitable types of memory.

In order to provide a context for the various aspects of the disclosedsubject matter, FIG. 10, and the following discussion, are intended toprovide a brief, general description of a suitable environment in whichthe various aspects of the disclosed subject matter can be implemented.While the subject matter has been described above in the general contextof computer-executable instructions of a computer program that runs on acomputer and/or computers, those skilled in the art will recognize thatthe various aspects also can be implemented in combination with otherprogram modules. Generally, program modules include routines, programs,components, data structures, etc. that perform particular tasks and/orimplement particular abstract data types. For example, in memory (suchas memory 404) there can be software, which can instruct a processor(such as processor 406) to perform various actions. The processor can beconfigured to execute the instructions in order to implement theanalysis of determining assignments for data streams transmitted to oneor more devices, suppressing inter-cell interference, and/or suppressingintra-cell interference.

Moreover, those skilled in the art will understand that the variousaspects can be practiced with other computer system configurations,including single-processor or multiprocessor computer systems,mini-computing devices, mainframe computers, as well as personalcomputers, base stations, hand-held computing devices or user equipment,such as a tablet, phone, watch, and so forth, processor-basedcomputers/systems, microprocessor-based or programmable consumer orindustrial electronics, and the like. The illustrated aspects can alsobe practiced in distributed computing environments where tasks areperformed by remote processing devices that are linked through acommunications network; however, some if not all aspects of the subjectdisclosure can be practiced on stand-alone computers. In a distributedcomputing environment, program modules can be located in both local andremote memory storage devices.

With reference to FIG. 10, a block diagram of a computing system 1000operable to execute the disclosed systems and methods is illustrated, inaccordance with an embodiment. Computer 1002 includes a processing unit1004, a system memory 1006, and a system bus 1008. System bus 1008couples system components including, but not limited to, system memory1006 to processing unit 1004. Processing unit 1004 can be any of variousavailable processors. Dual microprocessors and other multiprocessorarchitectures also can be employed as processing unit 1004.

System bus 1008 can be any of several types of bus structure(s)including a memory bus or a memory controller, a peripheral bus or anexternal bus, and/or a local bus using any variety of available busarchitectures including, but not limited to, industrial standardarchitecture, micro-channel architecture, extended industrial standardarchitecture, intelligent drive electronics, video electronics standardsassociation local bus, peripheral component interconnect, card bus,universal serial bus, advanced graphics port, personal computer memorycard international association bus, Firewire (institute of electricaland electronics engineers 1194), and small computer systems interface.

System memory 1006 includes volatile memory 1010 and nonvolatile memory1012. A basic input/output system, containing routines to transferinformation between elements within computer 1002, such as duringstart-up, can be stored in nonvolatile memory 1012. By way ofillustration, and not limitation, nonvolatile memory 1012 can includeread only memory, programmable read only memory, electricallyprogrammable read only memory, electrically erasable programmable readonly memory, or flash memory. Volatile memory 1010 can include randomaccess memory, which acts as external cache memory. By way ofillustration and not limitation, random access memory is available inmany forms such as dynamic random access memory, synchronous randomaccess memory, synchronous dynamic random access memory, double datarate synchronous dynamic random access memory, enhanced synchronousdynamic random access memory, Synchlink dynamic random access memory,and direct Rambus random access memory, direct Rambus dynamic randomaccess memory, and Rambus dynamic random access memory.

Computer 1002 also includes removable/non-removable,volatile/non-volatile computer storage media. In an implementation,provided is a non-transitory or tangible computer-readable mediumstoring computer-executable instructions that, in response to execution,cause a system comprising a processor to perform operations. Theoperations can include determining assignments for data streamstransmitted by one or more devices in a multiple-input multiple-outputcommunications network. The operations can also include suppressinginter-cell interference and suppressing intra-cell interference.According to an aspect, suppressing intra-cell interference comprisessuppressing the intra-cell interference on a per cell basis.

In an implementation, determining the assignments can comprisemaximizing a sum of a function applied to the data streams. In anotherimplementation, determining the assignments can comprise initializing astream assignment policy and determining whether interference alignmentis applicable to the data streams based on the stream assignment policy.

According to an implementation, the initializing comprises setting thestream assignment policy for a mobile device in communication with themultiple-input multiple-output network to be a number of data streamsrequested by the mobile device.

Suppressing the inter-cell interference can include updatingintermediate precoders and decorrelators, according to an aspect.According to another aspect, suppressing the inter-cell interference caninclude updating intermediate precoders and decorrelators andsuppressing intra-cell interference can include further adjusting theintermediate precoders.

According to an implementation, the one or more devices of themultiple-input multiple-output network comprise a combination of cells,user devices, and antennas. In some implementations, the one or moredevices of the multiple-input multiple-output network comprise a threeor more cells. In a further implementation, the operations can includezero forcing the inter-cell interference and the intra-cellinterference.

FIG. 10 illustrates, for example, disk storage 1014. Disk storage 1014includes, but is not limited to, devices such as a magnetic disk drive,floppy disk drive, tape drive, Jaz drive, Zip drive, superdisk drive,flash memory card, or memory stick. In addition, disk storage 1014 caninclude storage media separately or in combination with other storagemedia including, but not limited to, an optical disk drive such as acompact disk read only memory device, compact disk recordable drive,compact disk rewritable drive or a digital versatile disk read onlymemory drive. To facilitate connection of the disk storage 1014 tosystem bus 1008, a removable or non-removable interface can be used,such as interface component 1016.

It is to be noted that FIG. 10 describes software that acts as anintermediary between users and computer resources described in asuitable operating environment. Such software includes an operatingsystem 1018. Operating system 1018, which can be stored on disk storage1014, acts to control and allocate resources of computer system 1002.System applications 1020 can take advantage of the management ofresources by operating system 1018 through program modules 1022 andprogram data 1024 stored either in system memory 1006 or on disk storage1014. It is to be understood that the disclosed subject matter can beimplemented with various operating systems or combinations of operatingsystems.

A user can enter commands or information, for example through interfacecomponent 1016, into computer system 1002 through input device(s) 1026.Input devices 1026 include, but are not limited to, a pointing devicesuch as a mouse, trackball, stylus, touch pad, keyboard, microphone,joystick, game pad, satellite dish, scanner, TV tuner card, digitalcamera, digital video camera, web camera, and the like. These and otherinput devices connect to processing unit 1004 through system bus 1008through interface port(s) 1028. Interface port(s) 1028 include, forexample, a serial port, a parallel port, a game port, and a universalserial bus. Output device(s) 1030 use some of the same type of ports asinput device(s) 1026.

Thus, for example, a universal serial bus port can be used to provideinput to computer 1002 and to output information from computer 1002 toan output device 1030. Output adapter 1032 is provided to illustratethat there are some output devices 1030, such as monitors, speakers, andprinters, among other output devices 1030, which use special adapters.Output adapters 1032 include, by way of illustration and not limitation,video and sound cards that provide means of connection between outputdevice 1030 and system bus 1008. It is also noted that other devicesand/or systems of devices provide both input and output capabilitiessuch as remote computer(s) 1034.

Computer 1002 can operate in a networked environment using logicalconnections to one or more remote computers, such as remote computer(s)1034. Remote computer(s) 1034 can be a personal computer, a server, arouter, a network computer, a workstation, a microprocessor basedappliance, a peer device, or other common network node and the like, andcan include many or all of the elements described relative to computer1002.

For purposes of brevity, only one memory storage device 1036 isillustrated with remote computer(s) 1034. Remote computer(s) 1034 islogically connected to computer 1002 through a network interface 1038and then physically connected through communication connection 1040.Network interface 1038 encompasses wire and/or wireless communicationnetworks such as local area networks and wide area networks. Local areanetwork technologies include fiber distributed data interface, copperdistributed data interface, Ethernet, token ring and the like. Wide areanetwork technologies include, but are not limited to, point-to-pointlinks, circuit switching networks such as integrated services digitalnetworks and variations thereon, packet switching networks, and digitalsubscriber lines.

Communication connection(s) 1040 refer(s) to hardware/software employedto connect network interface 1038 to system bus 1008. Whilecommunication connection 1040 is shown for illustrative clarity insidecomputer 1002, it can also be external to computer 1002. Thehardware/software for connection to network interface 1038 can include,for example, internal and external technologies such as modems,including regular telephone grade modems, cable modems and DSL modems,ISDN adapters, and Ethernet cards.

It is to be noted that aspects, features, or advantages of the aspectsdescribed in the subject specification can be exploited in substantiallyany communication technology. For example, 4G technologies, Wi-Fi,worldwide interoperability for microwave access, Enhanced gatewaygeneral packet radio service, third generation partnership project longterm evolution, third generation partnership project 2 ultra mobilebroadband, third generation partnership project universal mobiletelecommunication system, high speed packet access, high-speed downlinkpacket access, high-speed uplink packet access, global system for mobilecommunication edge radio access network, universal mobiletelecommunication system terrestrial radio access network, and/or longterm evolution advanced. Additionally, substantially all aspectsdisclosed herein can be exploited in legacy telecommunicationtechnologies, such as, for example, global system for mobilecommunication. In addition, mobile as well non-mobile networks (e.g.,Internet, data service network such as Internet protocol television) canexploit aspects or features described herein.

Various aspects or features described herein can be implemented as amethod, apparatus, or article of manufacture using standard programmingand/or engineering techniques. In addition, various aspects disclosed inthe subject specification can also be implemented through programmodules stored in a memory and executed by a processor, or othercombination of hardware and software, or hardware and firmware.

Other combinations of hardware and software or hardware and firmware canenable or implement aspects described herein, including the disclosedmethod(s). The term “article of manufacture” as used herein is intendedto encompass a computer program accessible from any computer-readabledevice, carrier, or media. For example, computer readable media caninclude but are not limited to magnetic storage devices (e.g., harddisk, floppy disk, magnetic strips . . . ), optical discs (e.g., compactdisc, digital versatile disc, blu-ray disc . . . ), smart cards, andflash memory devices (e.g., card, stick, key drive . . . ).

Computing devices can include a variety of media, which can includecomputer-readable storage media or communications media, which two termsare used herein differently from one another as follows.

Computer-readable storage media can be any available storage media thatcan be accessed by the computer and includes both volatile andnonvolatile media, removable and non-removable media. By way of example,and not limitation, computer-readable storage media can be implementedin connection with any method or technology for storage of informationsuch as computer-readable instructions, program modules, structureddata, or unstructured data. Computer-readable storage media can include,but are not limited to, random access memory, read only memory,electrically erasable programmable read only memory, flash memory orother memory technology, compact disk read only memory, digitalversatile disk or other optical disk storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or other tangible and/or non-transitory media which can be used to storedesired information. Computer-readable storage media can be accessed byone or more local or remote computing devices, for example, via accessrequests, queries or other data retrieval protocols, for a variety ofoperations with respect to the information stored by the medium.

Communications media can embody computer-readable instructions, datastructures, program modules or other structured or unstructured data ina data signal such as a modulated data signal, for example, a carrierwave or other transport mechanism, and includes any information deliveryor transport media. The term “modulated data signal” or signals refersto a signal that has one or more of its characteristics set or changedin such a manner as to encode information in one or more signals. By wayof example, and not limitation, communication media include wired media,such as a wired network or direct-wired connection, and wireless mediasuch as acoustic, RF, infrared and other wireless media.

It is noted that aspects or features of the disclosed embodiments can beexploited in substantially any wireless communication technology. Suchwireless communication technologies can include universal mobiletelecommunication system, code division multiple access, Wi-Fi,worldwide interoperability for microwave access, gateway general packetradio service, enhanced gateway general packet radio service, thirdgeneration partnership project long term evolution, third generationpartnership project 2 ultra mobile broadband, high speed packet access,evolved high speed packet access, high-speed downlink packet access,high-speed uplink packet access, Zigbee, or another IEEE 802.XXtechnology. Additionally, substantially all aspects disclosed herein canbe exploited in legacy telecommunication technologies.

What has been described above includes examples of systems and methodsthat provide advantages of the one or more aspects. It is, of course,not possible to describe every conceivable combination of components ormethods for purposes of describing the aspects, but one of ordinaryskill in the art may recognize that many further combinations andpermutations of the claimed subject matter are possible. Furthermore, tothe extent that the terms “includes,” “has,” “possesses,” and the likeare used in the detailed description, claims, and drawings, such termsare intended to be inclusive in a manner similar to the term“comprising” as “comprising” is interpreted when employed as atransitional word in a claim.

As used in this application, the terms “component”, “system”, and thelike are intended to refer to a computer-related entity or an entityrelated to an operational apparatus with one or more specificfunctionalities, wherein the entity can be either hardware, acombination of hardware and software, software, or software inexecution. As an example, a component may be, but is not limited tobeing, a process running on a processor, a processor, an object, anexecutable, a thread of execution, computer-executable instructions, aprogram, and/or a computer. By way of illustration, both an applicationrunning on a server or network controller, and the server or networkcontroller can be a component. One or more components may reside withina process and/or thread of execution and a component may be localized onone computer and/or distributed between two or more computers. Also,these components can execute from various computer readable media havingvarious data structures stored thereon. The components may communicatevia local and/or remote processes such as in accordance with a signalhaving one or more data packets (e.g., data from one componentinteracting with another component in a local system, distributedsystem, and/or across a network such as the Internet with other systemsvia the signal). As another example, a component can be an apparatuswith specific functionality provided by mechanical parts operated byelectric or electronic circuitry, which is operated by a software, orfirmware application executed by a processor, wherein the processor canbe internal or external to the apparatus and executes at least a part ofthe software or firmware application. As yet another example, acomponent can be an apparatus that provides specific functionalitythrough electronic components without mechanical parts, the electroniccomponents can include a processor therein to execute software orfirmware that confers at least in part the functionality of theelectronic components. As further yet another example, interface(s) caninclude input/output components as well as associated processor,application, or application programming interface components.

The term “set”, “subset”, or the like as employed herein excludes theempty set (e.g., the set with no elements therein). Thus, a “set”,“subset”, or the like includes one or more elements or periods, forexample. As an illustration, a set of periods includes one or moreperiods; a set of transmissions includes one or more transmissions; aset of resources includes one or more resources; a set of messagesincludes one or more messages, and so forth.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form.

What is claimed is:
 1. A system, comprising: a memory to storeinstructions; and a processor, communicatively coupled to the memory,that facilitates execution of the instructions to perform operations,comprising: determining a respective assignment of each of a pluralityof data streams transmitted to one or more devices in a multiple-inputmultiple-output cellular network having partial connectivity resultingfrom heterogeneous path losses between a base station device and amobile device, wherein the determining the respective assignment of eachof the plurality of data streams is based on interference alignmentfeasibility status information and a joint precoder and decorrelatordesign, wherein the interference alignment feasibility statusinformation is determined based on a rank of a corresponding jointprecoder and decorrelator design relative to a data stream of theplurality of data streams, and wherein a value of the correspondingjoint precoder and decorrelator design is determined based on the rank;and suppressing both inter-cell interference and intra-cell interferenceindependent of multiple time slots or multiple frequency blocks.
 2. Thesystem of claim 1, wherein the determining the respective assignment ofeach of the plurality of data streams comprises maximizing a sum of afunction applied to the plurality of data streams.
 3. The system ofclaim 1, wherein the determining the respective assignment of each ofthe plurality of data streams comprises: initializing a streamassignment policy; and determining whether interference alignment isapplicable to the plurality of data streams based on the streamassignment policy.
 4. The system of claim 3, wherein the initializingcomprises setting the stream assignment policy for a mobile device incommunication with the multiple-input multiple-output cellular networkto be a number of data streams requested by the mobile device.
 5. Thesystem of claim 1, wherein the suppressing the inter-cell interferencecomprises updating intermediate precoders and decorrelators.
 6. Thesystem of claim 1, wherein the suppressing the inter-cell interferencecomprises updating intermediate precoders and decorrelators and thesuppressing intra-cell interference comprises further adjusting theintermediate precoders.
 7. The system of claim 1, wherein the one ormore devices of the multiple-input multiple-output cellular networkcomprise a combination of cells, user devices, and antennas.
 8. Thesystem of claim 1, wherein the one or more devices of the multiple-inputmultiple-output cellular network comprises three or more cells.
 9. Thesystem of claim 1, wherein the inter-cell interference and theintra-cell interference are produced by the transmitted data streams.10. A method, comprising: evaluating, by a system comprising aprocessor, a feasibility measurement of an interference alignment statusof a set of communication links of a communications network experiencingquasi-static fading as a result of heterogeneous path losses between abase station device and a mobile device, wherein the set ofcommunication links comprises a plurality of data streams carried on amix of defined communication links and undefined communication links andwherein an interference alignment of the domain interference alignmentstatus is determined to be of polynomial complexity; distinguishing, bythe system, the defined communication links from the undefinedcommunication links based on the feasibility measurement, wherein thefeasibility measurement is based on a rank of a corresponding jointprecoder and decorrelator design for a communication link of thecommunication links, and wherein a value of the corresponding jointprecoder and decorrelator design is based on the rank; suppressing, bythe system, a first interference caused by the defined communicationlinks; and suppressing, by the system, a second interference caused bythe undefined communication links that is different from the firstinterference.
 11. The method of claim 10, wherein the communicationsnetwork is a multiple-input multiple-output communications networkcomprising an arbitrary number of cells, user devices, and antennas. 12.The method of claim 10, further comprising concurrently zero forcing, bythe system, the first interference and the second interference.
 13. Themethod of claim 10, where the suppressing the first interference causedby the defined communication links comprises suppressing the firstinterference on a per cell basis.
 14. The method of claim 10, whereinthe evaluating comprises determining a network device of thecommunications network is configured to operate with application of aninterference alignment.
 15. The method of claim 10, wherein theevaluating comprises determining assignments for a first set of datastreams of the undefined communication links and a second set of datastreams of the defined communication links, and wherein the first set ofdata streams comprise at least three data streams, and furthercomprising maximizing a degree of freedom of a network device of thecommunications network.
 16. The method of claim 15, wherein theevaluating comprises: initializing a stream assignment policy comprisingsetting the stream assignment policy to be a number of streams requestedby each mobile device communicating with network devices of thecommunications network; and determining a practicability of interferencealignment within the communications network.
 17. The method of claim 15,wherein the suppressing the first interference comprises updatingintermediate precoders and decorrelators and the suppressing the secondinterference comprises adjusting the intermediate precoders after theupdating.
 18. A method, comprising: determining, by a system comprisinga processor, a feasibility related to assignments for a plurality ofdata streams transmitted by devices in a multiple-input multiple-outputmobile device network with heterogeneous path losses between a basestation device and a mobile device, the determining comprisingmaximizing a sum of a function of the data streams of the multiple-inputmultiple-output mobile device network based on interference alignmentfor a plurality of nodes comprised in the multiple-input multiple-outputmobile device network wherein the determining the feasibility comprisesdetermining the feasibility based on a rank of a corresponding jointprecoder and decorrelator design relative to a data stream of theplurality of data streams, and wherein a value of the correspondingjoint precoder and decorrelator design is determined based on the rank;suppressing inter-cell interference and suppressing intra-cellinterference independent of multiple time slots or multiple frequencyblocks, wherein the multiple-input multiple-output mobile device networkcomprises three or more cells.
 19. The method of claim 18, wherein thesuppressing inter-cell interference comprises updating intermediateprecoders and decorrelators and the suppressing intra-cell interferencecomprises further adjusting the intermediate precoders.
 20. The methodof claim 18, wherein the suppressing intra-cell interference comprisessuppressing the intra-cell interference on a per cell basis.